Correlation between surface roughness of plasma-sprayed chromium oxide coatings and powder grain size distribution: a fractal approach Guido Reisel a , Robert B. Heimann b, * a Institute for Composite Materials and Surface Technology, Technische Universita ¨t Chemnitz, Erfenschlager Str. 73, D-09125 Chemnitz, Germany b Department of Mineralogy, Technische Universita ¨t Bergakademie Freiberg, Brennhausgasse 14, D-09596 Freiberg, Germany Received 13 June 2003; accepted in revised form 14 January 2004 Available online 27 March 2004 Abstract Attempts were made to correlate the arithmetic mean surface roughness R a and the 10-point height values R z of atmospheric plasma-sprayed (APS) chromium oxide coatings with fractal properties such as the relative area for 2 Am 2 patch size (RAPS), the smooth-rough crossover (SRC) and the area-scaled fractal complexity (ASFC). In particular, the measured surface roughness of the coatings correlates with high statistical probability with the grain size distribution of the selected spray powders. It was found that the SRC value is useful to characterize the low and high cutoff values of the grain size distribution of thermal spray powders. Hence fractal analysis is a potential analytical tool to quantify the geometric complexity of the surface structure of plasma-sprayed coatings as a function of scale of observation. D 2004 Elsevier B.V. All rights reserved. Keywords: Fractal properties; Chromium oxide; Atmospheric plasma spraying; Surface roughness; Powder grain size; Patchwork method 1. Introduction Fractal geometry is a natural description of disordered objects ranging from macromolecules and self-similar vegetables (Broccoli Romanesco) to cloud shapes and topographical features of the earth’s surface such as coast lines and mountain ranges [1]. These objects often display ‘dilatation symmetry’, i.e. they look geometrically self- similar under transformation of scale. The fractality of many structures can be described by a single parameter D, the fractal dimension that is defined as the exponent that relates the mass of an object M to its size R, hence MfR D [2]. This relation holds for smooth Euclidian objects such as rods, discs and spheres with D equal to 1, 2 and 3, respectively (mass fractals). However, surface fractals are uniformly dense but with a rough surface. They are self-similar in the sense that if the surface is magnified, its geometrical features are scale-invariant. This surface self-similarity can be expressed analogously by SfR D(S) with S=surface area and D(S)=surface fractal dimension varying between 2 for ideally smooth and 2<D(S)<3 for fractally rough surfaces. Hence D(S) can be taken as a measure of surface roughness [3,4]. It should be empha- sized that fractals describe only the principle of ordering but fail to provide information on the mechanism that leads to this ordering. Nevertheless, it is tempting to investigate whether plasma-sprayed coatings can be treated as fractal surfaces, and in which way their surface rough- ness depends on the grain size distribution of the initial spray powder as well as on the intrinsic plasma spray parameters. This information is essential to estimate the adhesive strength of thermally sprayed coatings that is well-known to depend crucially on surface roughness. Hard plasma-sprayed chromium oxide coatings are being applied when corrosion resistance is required in addition to abrasion resistance, i.e. in the case of strongly synergistic corrabrasion in aggressive environments. Con- sequently such coatings find use for joints and bearings in sliding contact, in water and sludge pumps, for steel rollers for ore classification and smooth top coats for printing 0257-8972/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.surfcoat.2004.01.018 * Corresponding author. Tel.: +49-3731-392666; fax: +49-3731- 393129. E-mail address: heimann@mineral.tu-freiberg.de (R.B. Heimann). www.elsevier.com/locate/surfcoat Surface & Coatings Technology 185 (2004) 215– 221